Riemann 映射与单连通区域分类

设G为复平面上一个单连通区域及φ为G的Riemann 映射. 本文通过φ是否属于G上多项式在不同拓扑下的闭包的情况对G进行分类. 特别地, 我们对已知的几类单连通给出了刻画.

Riemann map and classifications for simply connected domains

Let G be a simply connected domain in the complex plane and φ be its Riemann map. In this article, we give classifications for some known simply connected domains by investigating if φ belongs to the closure of the polynomials in certian topologies. Especially, we give new characterizations for some well-known domains.